Kernel Methods for Causal Functions: Dose Response Curves and Heterogeneous Treatment Effects

We propose a family of estimators based on kernel ridge regression for nonparametric causal functions such as the dose response curve, heterogeneous treatment effect, and incremental response curve. We assume selection on observable covariates. Treatment and covariates may be discrete or continuous and may take values in general spaces. We reduce causal estimation to combinations of kernel ridge regressions, which have closed form solutions and are easily computed by matrix operations, unlike other machine learning paradigms. We prove uniform consistency of the causal function estimators, with finite sample convergence rates that are the sums of minimax optimal rates for kernel ridge regression. In nonlinear simulations with many covariates, we demonstrate state-of-the-art performance despite the relative simplicity of our proposed approach. We estimate the dose response curve, heterogeneous treatment effect, and incremental response curve of the US Jobs Corps training program. As extensions, we generalize our main results to counterfactual distributions and to causal functions identified by Pearl's front and back door criteria.